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Lesson Menu Five-Minute Check (over Lesson 4–4) CCSS Then/Now New Vocabulary Postulate 4.3: Angle-Side-Angle (ASA) Congruence Example 1:Use ASA to Prove Triangles Congruent Theorem 4.5:Angle-Angle-Side (AAS) Congruence Example 2:Use AAS to Prove Triangles Congruent Example 3:Real-World Example: Apply Triangle Congruence Concept Summary: Proving Triangles Congruent

Over Lesson 4–4 5-Minute Check 1 A.SSS B.ASA C.SAS D.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4 5-Minute Check 2 A.SSS B.ASA C.SAS D.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4 5-Minute Check 3 A.SAS B.AAS C.SSS D.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4 5-Minute Check 4 A.SSA B.ASA C.SSS D.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4 5-Minute Check 5 A.AAA B.SAS C.SSS D.not possible Determine which postulate can be used to prove that the triangles are congruent. If it is not possible to prove congruence, choose not possible.

Over Lesson 4–4 5-Minute Check 6 Given  A   R, what sides must you know to be congruent to prove ΔABC  ΔRST by SAS? A. B. C. D.

CCSS Content Standards G.CO.10 Prove theorems about triangles. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. 5 Use appropriate tools strategically.

Then/Now You proved triangles congruent using SSS and SAS. Use the ASA Postulate to test for congruence. Use the AAS Theorem to test for congruence.

Vocabulary included side

Concept

Example 1 Use ASA to Prove Triangles Congruent Write a two-column proof.

Example 1 Use ASA to Prove Triangles Congruent 4.Alternate Interior Angles 4.  W   E Proof: StatementsReasons 1. Given 1.L is the midpoint of WE. ____ 3. Given Midpoint Theorem 2. 5.Vertical Angles Theorem 5.  WLR   ELD 6.ASA 6. ΔWRL  ΔEDL

Example 1 A.SSSB. SAS C.ASAD. AAS Fill in the blank in the following paragraph proof.

Concept

Example 2 Use AAS to Prove Triangles Congruent Write a paragraph proof. Proof:  NKL   NJM, KL  MN, and  N   N by the Reflexive property. Therefore, ΔJNM  ΔKNL by AAS. By CPCTC, LN  MN. _____ _____

Example 2 A.SSSB. SAS C.ASAD. AAS Complete the following flow proof.

Example 3 Apply Triangle Congruence MANUFACTURING Barbara designs a paper template for a certain envelope. She designs the top and bottom flaps to be isosceles triangles that have congruent bases and base angles. If EV = 8 cm and the height of the isosceles triangle is 3 cm, find PO.

Example 3 Apply Triangle Congruence ΔENV  ΔPOL by ASA. In order to determine the length of PO, we must first prove that the two triangles are congruent. ____ NV  EN by definition of isosceles triangle ____ EN  PO by CPCTC. ____ NV  PO by the Transitive Property of Congruence. ____ Since the height is 3 centimeters, we can use the Pythagorean theorem to calculate PO. The altitude of the triangle connects to the midpoint of the base, so each half is 4. Therefore, the measure of PO is 5 centimeters. Answer: PO = 5 cm

Example 3 A.SSS B.SAS C.ASA D.AAS The curtain decorating the window forms 2 triangles at the top. B is the midpoint of AC. AE = 13 inches and CD = 13 inches. BE and BD each use the same amount of material, 17 inches. Which method would you use to prove ΔABE  ΔCBD?

Concept

End of the Lesson